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jonny [76]
3 years ago
13

Assume that the lines that appear to be tangent are tangent p is the center if each circle find x. ​

Mathematics
1 answer:
Elodia [21]3 years ago
4 0

Answer:

Step-by-step explanation:

Problem One

All quadrilaterals have angles that add up to 360 degrees.

Tangents touch the circle in such a way that the radius and the tangent form a  right angle at the point of contact.

Solution

x + 115 + 90 + 90 = 360

x + 295 = 360

x + 295 - 295 = 360 - 295

x = 65

Problem Two

From the previous problem, you know that where the 6 and 8 meet is a right angle.

Therefore you can use a^2 + b^2 = c^2

a = 6

b =8

c = ?

6^2 + 8^2 = c^2

c^2 = 36 + 64

c^2 = 100

sqrt(c^2) = sqrt(100)

c = 10

x = 10

Problem 3

No guarantees on this one. I'm not sure how the diagram is set up. I take the 4 to be the length from the bottom of the line marked 10 to the intersect point of the tangent with the circle.

That means that the measurement left is 10 - 4 = 6

x and 6 are both tangents from the upper point of the line marked 10.

Therefore x = 6

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(High points) please solve with explanation
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Answer:

The area and the perimeter of the picture are:

  • <u>Area = 160 cm^2</u>
  • <u>Perimeter = 67.31 cm</u>

Step-by-step explanation:

To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:

  • Area of a rectangle = base * height

As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:

  • Area of a rectangle = 16 cm * 12 cm
  • Area of a rectangle = 192 cm^2

Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:

  • Area of a triangle = (base * height) / 2

The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:

  • Area of a triangle = (8 cm * 8 cm) / 2
  • Area of a triangle = (64 cm^2) / 2
  • Area of a triangle = 32 cm^2

We subtract to the found area:

  • Area of the picture = 192 cm^2 - 32 cm^2
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To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:

  • a^{2}+b^{2}=c^{2}

Where:

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  • b = Adjacent leg (8 cm)

So, we replace in the theorem:

  • a^{2}+b^{2}=c^{2}
  • (8 cm)^{2}+(8cm)^{2}=c^{2} (and we clear c)
  • \sqrt{(8 cm)^{2}+(8cm)^{2}} =c
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  • \sqrt{128cm^{2}} =c
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At last, we add all the sides of the picture begining by the base and going by the left side:

  • Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
  • <u>Perimeter of the picture = 67.31 cm approximately</u>.
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You would add 10.3 and 5.9 which would equal 16.2, and subtract that from 20 and change that decimal into a fraction, which would be 19/50
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